The Increasing Families of Sets Generated by Self-dual Clutters

TL;DR

This paper investigates bounds on the number of k-sets in increasing families generated by self-dual clutters, utilizing KKS inequalities to explore combinatorial properties of these structures.

Contribution

It establishes bounds on k-sets in families generated by self-dual clutters using KKS inequalities, advancing understanding of their combinatorial structure.

Findings

Bounds on the number of k-sets established

Application of KKS inequalities to self-dual clutters

Insights into the structure of increasing families

Abstract

Using the KKS inequalities, we establish bounds on the numbers of $k$-sets in the increasing families generated by self-dual clutters (i.e., clutters $\mathcal{A}$ that coincide with the blockers $\mathfrak{B}(\mathcal{A})$) on their ground set of even cardinality.